An Explicit Construction of the Underlying Laminated Microstructure of the Least Compliant Elastic Bodies.

The paper discusses the problem of recovery of the microstructure of the least compliant bodies of non-homogeneous optimal isotropic properties predicted by the Isotropic Material Design method. The three-dimensional microstructure is assumed as constructed by a subsequent lamination process in which two isotropic materials of ordered properties are used, the process being repeated three or six times, subsequently. The Hooke tensors closest to the optimal ones are found by making use of the analytical Francfort--Murat formulae for effective moduli of third and sixth rank sequential laminates. The ability to model an auxetic behavior within the subdomains where the optimal Poisson's ratio assumes negative values is also shown. [ABSTRACT FROM AUTHOR]